Presentation length and Simon's conjecture
Geometric Topology
2011-05-19 v3
Abstract
In this paper, we show that any knot group maps onto at most finitely many knot groups. This gives an affirmative answer to a conjecture of J. Simon. We also bound the diameter of a closed hyperbolic 3-manifold linearly in terms of the presentation length of its fundamental group, improving a result of White.
Cite
@article{arxiv.1006.5262,
title = {Presentation length and Simon's conjecture},
author = {Ian Agol and Yi Liu},
journal= {arXiv preprint arXiv:1006.5262},
year = {2011}
}
Comments
34 pages, 3 figures, fixed some errors, especially in the proof of Prop. 7.2. Final version to appear in Journal of the American Mathematical Society